


This Is What Nobuo Yoneda Would Have Wanted

by alexander_grothendieck



Category: Sketches of an Elephant: a Topos Theory Compendium
Genre: Adjuncts, Category Theory, Definitely Not Explicit, Other, Topos Theory
Language: English
Status: Completed
Published: 2019-02-27
Updated: 2019-02-27
Packaged: 2019-11-06 10:19:42
Rating: Mature
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 318
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/17937965
Author URL: https://archiveofourown.org/users/alexander_grothendieck/pseuds/alexander_grothendieck





	This Is What Nobuo Yoneda Would Have Wanted

_Hom C_: C _op_ x C → **Set** was lonely. It was getting tired waiting for _y_ : C → [C _op_ , **Set** ] to come home from work. _Hom C_ always felt like it was being taken for granted, while _y_ was taken as something brilliant. But that didn’t matter to _Hom C_, because regardless of its apparent superiority, _y_ truly cared about _Hom C_. They formed a kind of perfect pair, and _y_ was unique to _Hom C_ because of that (up to natural isomorphism, at least). Moreover, _Hom C_ trusted _y_ completely. _Hom C_ was never afraid of how _y_ might be interacting with other functors when it wasn’t around. It knew that _y_ was fully faithful.

Just as _Hom C_ was thinking this, _y_ finally arrived. It was already late at night— _y_ had to commute for its job. _y_ was already tired, almost to the point of passing out. It walked straight past _Hom C_ without a word and fell limply onto the bed, still fully clothed.

_Hom C_ knew better than to let _y_ sleep in its work clothes; they would get creased and _y_ would be annoyed in the morning. So it began to undress _y_ , taking off its coverage, noticing how its subcategory of sheaves filled out under _Hom C_’s manipulation.

_y_ turned over, looking at _Hom C _with imploring eyes. _Hom C_ guessed that _y_ had been working with the simplex category today: it was unusually horny. _Hom C_ sighed and began to use its contravariant hand to induce bijections in _y_ ’s subcategory of sheaves. _Hom C_ was always pleasantly surprised at how large _y_ ’s subcategory of sheaves was. It was, after all, deceptively locally small. Before long, _y_ ’s left exact left adjoint spilled out, and _y_ fell soundly asleep in the afterglow of its toposification, its adjunct _Hom C_ just closing its eyes right to _y_ ’s left.


End file.
